Greg Voth

Fluid Particle Accelerations in Fully Developed Turbulence

The motion of fluid particles as they are pushed along erratic trajectories by fluctuating pressure gradients is fundamental to transport and mixing in turbulence. It is essential in cloud formation and atmospheric transport, processes in stirred chemical reactors and combustion systems, and in the industrial production of nanoparticles. The concept of particle trajectories has been used successfully to describe mixing and transport in turbulence, but issues of fundamental importance remain unresolved. One such issue is the Heisenberg–Yaglom prediction of fluid particle accelerations, based on the 1941 scaling theory of Kolmogorov. Here we report acceleration measurements using a detector adapted from high-energy physics to track particles in a laboratory water flow at Reynolds numbers up to 63,000. We find that, within experimental errors, Kolmogorov scaling of the acceleration variance is attained at high Reynolds numbers. Our data indicate that the acceleration is an extremely intermittent variable—particles are observed with accelerations of up to 1,500 times the acceleration of gravity (equivalent to 40 times the root mean square acceleration). We find that the acceleration data reflect the anisotropy of the large-scale flow at all Reynolds numbers studied.

Measurement of particle accelerations in fully developed turbulence

We use silicon strip detectors (originally developed for the CLEO III high-energy particle physics experiment) to measure fluid particle trajectories in turbulence with temporal resolution of up to 70000 frames per second. This high frame rate allows the Kolmogorov time scale of a turbulent water flow to be fully resolved for 140 [ges ] R λ [ges ] 970. Particle trajectories exhibiting accelerations up to 16000 m s −2 (40 times the r.m.s. value) are routinely observed. The probability density function of the acceleration is found to have Reynolds-number-dependent stretched exponential tails. The moments of the acceleration distribution are calculated. The scaling of the acceleration component variance with the energy dissipation is found to be consistent with the results for low-Reynolds-number direct numerical simulations, and with the K41-based Heisenberg–Yaglom prediction for R λ [ges ] 500. The acceleration flatness is found to increase with Reynolds number, and to exceed 60 at R λ = 970. The coupling of the acceleration to the large-scale anisotropy is found to be large at low Reynolds number and to decrease as the Reynolds number increases, but to persist at all Reynolds numbers measured. The dependence of the acceleration variance on the size and density of the tracer particles is measured. The autocorrelation function of an acceleration component is measured, and is found to scale with the Kolmogorov time τ η .

Experimental Measurements of Stretching Fields in Fluid Mixing

The mixing of an impurity into a flowing fluid is an important process in many areas of science, including geophysical processes, chemical reactors, and microfluidic devices. In some cases, for example periodic flows, the concepts of nonlinear dynamics provide a deep theoretical basis for understanding mixing. Unfortunately, the building blocks of this theory, i.e. the fixed points and invariant manifolds of the associated Poincare map, have remained inaccessible to direct experimental study, thus limiting the insight that could be obtained. Using precision measurements of tracer particle trajectories in a two-dimensional fluid flow producing chaotic mixing, we directly measure the time-dependent stretching and compression fields. These quantities, previously available only numerically, attain local maxima along lines coinciding with the stable and unstable manifolds, thus revealing the dynamical structures that control mixing. Contours or level sets of a passive impurity field are found to be aligned parallel to the lines of large compression (unstable manifolds) at each instant. This connection appears to persist as the onset of turbulence is approached.

Lagrangian acceleration measurements at large Reynolds numbers

We report experimental measurements of Lagrangian accelerations in a turbulent water flow between counter-rotating disks for Taylor–Reynolds numbers 900<Rλ<2000. Particle tracks were recorded by imaging tracer particles onto a position sensitive photodiode, and Lagrangian information was obtained from fits to the position versus time data. Several challenges associated with extracting Lagrangian statistical quantities from particle tracks are addressed. The acceleration variance is obtained as a function of Reynolds number and shows good agreement with Kolmogorov (1941) scaling. The Kolmogorov constant for the acceleration variance is found to be a0=7±3.

Rotation Rate of Rods in Turbulent Fluid Flow

The rotational dynamics of anisotropic particles advected in a turbulent fluid flow are important in many industrial and natural settings. Particle rotations are controlled by small scale properties of turbulence that are nearly universal, and so provide a rich system where experiments can be directly compared with theory and simulations. Here we report the first three-dimensional experimental measurements of the orientation dynamics of rodlike particles as they are advected in a turbulent fluid flow. We also present numerical simulations that show good agreement with the experiments and allow extension to a wide range of particle shapes. Anisotropic tracer particles preferentially sample the flow since their orientations become correlated with the velocity gradient tensor. The rotation rate is heavily influenced by this preferential alignment, and the alignment depends strongly on particle shape.

Mixing rates and symmetry breaking in two-dimensional chaotic flow

We experimentally determine the mixing rate for a magnetically forced two-dimensional time-periodic flow exhibiting chaotic mixing. The mixing rate, defined as the rate of decay of the root-mean square concentration inhomogeneity, grows with Reynolds number, but does not increase at the onset of nonperiodic (weakly turbulent) flow. The mixing rate increases linearly with a second non-dimensional parameter, the typical path length of a fluid element in one forcing period. The breaking of time-reversal symmetry and spatial reflection symmetry substantially increases the mixing rates. A theory by Antonsen et al. that predicts mixing rates in terms of the measured Lyapunov exponents of the flow is tested and found to predict mixing rates that are too large by approximately a factor of 10; the discrepancy is traced to the fact that large scale transport rather than stretching of fluid elements is the dominant rate limiting step when the system is sufficiently large compared to the velocity correlation length. An effective diffusion model gives a good account of the measured mixing rates. Finally, the formation of persistent recurrent patterns (also called strange eigenmodes) is shown to arise from a combination of stretching and effective diffusion.

Shape-dependence of particle rotation in isotropic turbulence

We consider the rotation of neutrally buoyant axisymmetric particles suspended in isotropic turbulence. Using laboratory experiments as well as numerical and analytical calculations, we explore how particle rotation depends upon particle shape. We find that shape strongly affects orientational trajectories, but that it has negligible effect on the variance of the particle angular velocity. Previous work has shown that shape significantly affects the variance of the tumbling rate of axisymmetric particles. It follows that shape affects the spinning rate in a way that is, on average, complementary to the shape-dependence of the tumbling rate. We confirm this relationship using direct numerical simulations, showing how tumbling rate and spinning rate variances show complementary trends for rod-shaped and disk-shaped particles. We also consider a random but non-turbulent flow. This allows us to explore which of the features observed for rotation in turbulent flow are due to the effects of particle alignment i...

Alignment of vorticity and rods with Lagrangian fluid stretching in turbulence

Stretching in continuum mechanics is naturally described using the Cauchy–Green strain tensors. These tensors quantify the Lagrangian stretching experienced by a material element, and provide a powerful way to study processes in turbulent fluid flows that involve stretching such as vortex stretching and alignment of anisotropic particles. Analysing data from a simulation of isotropic turbulence, we observe preferential alignment between rods and vorticity. We show that this alignment arises because both of these quantities independently tend to align with the strongest Lagrangian stretching direction, as defined by the maximum eigenvector of the left Cauchy–Green strain tensor. In particular, rods approach almost perfect alignment with the strongest stretching direction. The alignment of vorticity with stretching is weaker, but still much stronger than previously observed alignment of vorticity with the eigenvectors of the Eulerian strain rate tensor. The alignment of strong vorticity is almost the same as that of rods that have experienced the same stretching.

Rotation and alignment of rods in two-dimensional chaotic flow

We study the dynamics of rod shaped particles in two-dimensional electromagnetically driven fluid flows. Two separate types of flows that exhibit chaotic mixing are compared: one with time-periodic flow and the other with constant forcing but nonperiodic flow. Video particle tracking is used to make accurate simultaneous measurements of the motion and orientation of rods along with the carrier fluid velocity field. These measurements allow a detailed comparison of the motion and orientation of rods with properties of the carrier flow. Measured rod rotation rates are in agreement with predictions for ellipsoidal particles based on the measured velocity gradients at the center of the rods. There is little dependence on length for the rods we studied (up to 53% of the length scale of the forcing). Rods are found to align weakly with the extensional direction of the strain-rate tensor. However, the alignment is much stronger with the direction of Lagrangian stretching defined by the eigenvectors of the Cauchy...

Using cavitation to measure statistics of low-pressure events in large-Reynolds-number turbulence

No completely satisfactory experimental technique exists for making noninvasive measurements of the pressure field in a turbulent flow. Conventional pressure sensors are typically unable to resolve the finest scales of intense turbulence. More fundamentally, conventional sensors usually measure the pressure on the wall of the container rather than in the bulk of the flow. Pressure probes can be constructed which extend into the flow and measure the pressure at a point, but these can perturb the flow and usually suffer from velocity contamination. In this paper, we report studies using cavitation to detect large negative pressure fluctuations in a turbulent water flow between counter-rotating disks. The large-Reynolds-number water flow is seeded with small gas bubbles and the hydrostatic pressure is adjusted so that negative pressure fluctuations go below the vapor pressure and trigger cavitation. The seed bubbles are a negligible perturbation to the system up until the moment that cavitation is triggered. The spatial and temporal resolution of the measurement is very high, and is set by the size, number density, and resonant frequencies of the seed bubbles. We use high-speed video imaging of the coherent pressure structures marked by cavitation as a way to visualize the low-pressure filaments. In addition, we study the probability distribution of large negative pressure fluctuations by measuring the light scattered from cavitating bubbles in a small region of the flow. From this we estimate the scaling with Reynolds number of the negative tail of the pressure distribution. The importance of the pressure in the equations of fluid motion has motivated many studies of the properties of the pressure field. 1‐4 Numerical simulations 5‐9 and experimental measurements from conventional pressure probes 10‐12 have found that the pressure distribution is skewed to negative pressures where there is an exponential tail. It has been shown analytically 13 that this does not necessarily indicate the presence of structures in the flow because even Gaussian velocity fields produce exponential pressure tails. However, a careful numerical study 7 finds that despite qualitative